Mathematical models of viral infection have been successfully applied to a number of problems on the periphery of the annual public health problem that is influenza. In the laboratory, mathematical models have aided the development of efficient vaccine production techniques and improved the quantitative characterization of antiviral drug action. Mathematical models have also improved our understanding of the course of the disease within human and animal hosts. Because these models serve as a bridge between the microscopic scale (where virus interacts with cell) and the macroscopic scale (where the infection is manifested as a disease) they will inevitably be applied in the future to pressing public health questions such as the estimation of virulence and fitness for emerging strains, the spread of drug resistance and, more generally, the connections between viral genotypic information and clinical data.